Q179 / 200 · Manipal (MET) 2010 · Physics

The time period of a geostationary satellite at a height 36000 km is 24 h . A spy satellite orbits earth at a height 6400 km . What will be the time period of spy satellite? [Radius of the earth $=6400 \mathrm{~km}$ ]

  • A
    5 h
  • Correct answer
    B
    4 h
  • C
    3 h
  • D
    12 h

Solution

From Kepler's third law of planetary motion $T^2 \propto R^3$ $\therefore \frac{T_2^2}{T_1^2}=\frac{R_2^3}{R_1^3}$ or $\frac{T_2^2}{(24)^2}=\left(\frac{6400+6400}{36000+6400}\right)^3$ or $T_2^2=(24)^2 \times\left(\frac{16}{53}\right)^3$ $\Rightarrow T_2=4 \mathrm{~h}$

Hence, the correct answer is option: 'B'.

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